This metric indicates that a vertex would remain in its own community as long as its internal pull is greater than the external pull or its internal neighbors are densely connected to each other, hence forming a near clique.
The Permanence for a network G is then defined as \(Perm(G) = \frac{\sum _{v \in V} Perm(v)}{\vert V \vert }\) .
The reasons behind choosing Permanence instead of other community scoring metrics such as (local) modularity [1]}, [2]}, conductance, cut-ratio [3]} are two-fold: (i) Permanence is a vertex-centric local metric which would enable us to update edges incrementally in order to change the network structure without looking into the entire network structure, and (ii) Permanence has been shown to be superior to other local and global scoring metrics for community detection [4]}.
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